Final answer:
A client on TPN presenting with shakiness and diaphoresis should have their blood glucose assessed next to check for possible hypoglycemia.
Step-by-step explanation:
A client who has been receiving total parenteral nutrition (TPN) and is now experiencing shakiness and is diaphoretic should have a blood glucose assessment performed next. These symptoms may indicate hypoglycemia, which can occur in patients receiving TPN because the infusion consists of high glucose contents. Monitoring the blood glucose level is a priority to determine if the patient requires an adjustment in their TPN formulation, or if they need interventions to correct potential hypoglycemia.